We present a new framework for describing multi-agent systems with hybrid interacting dynamics where the interaction between agents occurs at both the continuous and discrete levels. We formally define these multi-agent systems as Interconnected
Hybrid Systems and then recast fundamental hybrid concepts such as a hybrid metric, hybrid execution, and reachability in this new interconnected hybrid systems framework. We then prove a necessary and sufficient condition for the existence and uniqueness of the interconnected hybrid executions extending previous work on hybrid systems.